Pure Spin Currents and the Associated Electrical Voltage

Abstract

We present a generalize Landauer-Büttiker transport theory for multi-terminal spin transport in presence of spin-orbit interaction. It is pointed out that the presence of spin-orbit interaction results in equilibrium spin currents, since in presence of spin-orbit interaction spin is not a conserved quantitative. Further we illustrate the theory by applying it to a three terminal Y-shaped conductor. It is shown that when one of the terminal is a potential probe, there exist nonequilibrium pure spin currents without an accompanying charge current. It is shown that this pure spin currents causes a voltage drop which can be measured if the potential probe is ferromagnetic.PACS numbers: 72. 72.25.Dc, 72.25.Mk Producing and measuring spin currents is a major goal of spintronics. The standard way is to inject spin currents from a Ferromagnet into a semiconductor in a two terminal geometry [1]. However this has a drawback, due to conductivity mismatch, the polarization of injected current is rather small and it always has an accompanying charge current [2]. Also for any spintronics operation spin orbit interaction plays an important role, for e.g., in Datta-Das spin-transistor [3].In light of these development it would be interesting and highly desirable if one can produce spin currents intrinsically. One such possibility is provided by intrinsics spin-orbit interaction. Presence of impurity atom or defects gives rise to spin-orbit interaction of the form [4] [5], [6],where σ is a vector of Pauli matrices ,U(r) is potential due to defects or impurity atoms and k is the momentum wave vector of electrons and λ is spin-orbit interaction strength. For strictly two dimensional case for which the potential U(r) depends on x and y coordinates only the Hamiltonian commutes with σ z , hence z component of the spin is good quantum number. As is well know that this kind of spin-orbit interaction has a polarizing effect on particle scattering [7], i.e, when an unpolarized beam is scattered it gets polarized perpendicular to the plane of scattering. Further scattering of this polarized beam causes asymmetry in scattering processes, i.e. electrons with one particular spin direction, e.g., spin-up electrons have a larger probability to be scattered to the right compared to spin-down electrons [6], [7]. This property of spin-orbit scattering gives rise to novel effects like spin hall effect [4].Here in this article we show that the the above discussed property of spin-orbit scattering can be used to generate and measure spin-currents [5]. Consider a three terminal, two dimensional Y shaped conductor shown in Fig.1. The plane of conductor is xy. Since the conductor is two dimensional which fixes the scattering plane, the scattered electrons will be polarized along z axis (perpendicular to the scattering plane). However the polarization for the two branches of Y junction will be opposite [4]. Hence a three terminal structure would create spin currents from an unpolarized current in presence of spin-orbit interaction [6], [8]. Moreover...

Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

“…This picture also provides a direct microscopic proof that no equilibrium total spin currents, conjectured in Ref. 33, can actually appear in the leads of an unbiased V p = const. mesoscopic device in thermodynamic equilibrium, as demonstrated recently 16,50 within the LandauerBüittker approach which operates only with the total spin and charge currents in the leads.…”

“…15,16,33 In this formalism, one has to compute the spin-resolved transmission matrices connecting the spin-polarized asymptotic scattering states in semi-infinite ideal leads attached to the sample, 53 which requires the knowledge of only the elements of the retarded Green function matrix Eq. (44) between the sites of the sample which are adjacent to the leads (similar expressions in terms of only the retarded Green function between the sample edges are obtained for the total charge currents 40,43 ).…”

“…15,17 However, the theory of the mesoscopic spin Hall effect is formulated in terms of the Landauer-Büttiker-type transmission formalism 34 for spin currents, 15,16,33 which connects asymptotic scattering states in the leads without requiring any information about the quantum-mechanical probabilities for spin and charge propagation between the two points inside the sample. Technically, to obtain the spin Hall current flowing through the leads of a multiterminal device, one only needs the spin-dependent retarded real-space Green function connecting the sites residing in different leads and no information about its values between the points within the sample.…”

Topological Anderson insulator phenomena

“…Concerning for the scalar current flowing into the drain lead (12), (13), we can get the Landauer-Buttikker formula 28 , which leads to conductance in zero temprature…”

Mesoscopic Stern-Gerlach spin filter by nonuniform spin-orbit interaction

“…Several devices based on the SOI are proposed to have spin polarized carriers in semiconductor channel. 7,8,9,10,11,12,13 From experimental point of view, the spin polarization mechanism should be robust against disorder.One of the historical experiments of the spin separation is the Stern-Gerlach experiment. 14 They have considered a particle with spin propagating through the nonuniform magnetic field.…”